Figure 2.5 Contours of zonally and annually averaged radiative damping time-scale (days). (After Newman and Rosenfieid |55|.)
directions, while critically important to the distribution of trace gases in the stratosphere, are smaller than the zonal component of the wind velocity. The dominance of zonal flow means that the air tends to be well mixed in the zonal direction. In other words, air at different longitudes but the same latitude and altitude is more similar than air at different latitudes or different altitudes. For this reason, data from the same latitude and altitude but different longitudes are often averaged together to obtain a "zonal average". Many of the plots in this book are zonal averages (e.g. see Figure 2.5).
While flow in the stratosphere is predominantly zonal, individual air parcels can experience significant changes in their latitude on a time-scale of a day. Such displacements are caused by planetary-scale waves, and are often reversible, so that the air parcel will return to its original latitude after one to a few days. At a given latitude, one therefore often finds that some of the air parcels have a chemical composition characteristic of other latitudes. This means that latitude is often not the best choice of horizontal coordinate.
We have, however, a horizontal coordinate that is conserved during reversible meridional transport by planetary-scale waves. It is known as potential vorticity (PV) [56J. Thus, while the latitude of a parcel might change during transport by planetary-scale waves, its PV remains constant. Mathematically, PV is related to the curl of the wind field, the rotation of the Earth, and the local thermal gradient, and may be thought of conceptually as a fluid dynamical analog of angular momentum. PV is normally positive in the northern hemisphere and negative in the southern hemisphere, consistent with the sense of the Earth's rotation, and increases in absolute magnitude with latitude on surfaces of constant potential temperature. PV is conserved on time-scales similar to the time-scale over which potential temperature is conserved (Figure 2.5).
As a result, air at the same altitude and PV tends to be more similar than air at the same latitude, making PV a superior horizontal coordinate [57,58], For simplicity, PV is often expressed in units of equivalent latitude. The equivalent latitude of a PV value is the latitude circle that encloses the same area as the PV contour. Because of its convenience, equivalent latitude will be used frequently in this book—often in the context of a zonally averaged equivalent-latitude plot. In this type of plot, data at the same equivalent latitude and altitude are averaged together, regardless of longitude, to obtain a two-dimensional view of the atmosphere. Because equivalent latitude more accurately separates different air masses, this type of plot will better capture strong meridional gradients in the data—such as those found around the polar vortex (discussed in Chapter 7). Finally, it should be noted that equivalent latitude can be calculated from geophysical parameters other than PV [59,60|.
A long-lived tracer is a constituent that has a stratospheric lifetime of years or longer. The sources of most long-lived tracers are in the troposphere, while their sinks are primarily in the stratosphere. A good example is nitrous oxide (N20), which is produced near the surface through both natural and anthropogenic activities. It enters the stratosphere with a VMR of -310 ppbv, and it is destroyed in the middle and upper stratosphere. The local lifetime of N,0 is -100 years at 20 km, -10 years at 25 km, -1 year at 30 km. and a few months at 40 km.
The distribution of N20 is in general determined by a combination of chemistry and dynamics. Figure 2.6 shows a zonal average distribution of the N20 VMR. Note the strong gradients in N20 VMR in both the horizontal and vertical. The vertical gradient results primarily from the rapidly increasing loss rate of N20 with altitude combined with relatively slow vertical transport in the stratosphere. The horizontal gradients occur in regions of slow horizontal mixing. This will be discussed further in Chapter 5.
Because of these gradients, we can use the abundance of N20 to help determine the recent history of air masses [61,62]. The tropical lower stratosphere, for example, contains N20 VMRs greater than -250 ppbv, a higher value than found at higher latitudes or altitudes. Thus, a measurement of N20 VMR of greater than 250 ppbv in the mid-latitudes suggests that this air is of tropical origin and has recently been transported to mid-latitudes. Similarly, an observation of lower stratospheric air with less than 100 ppbv of N20 suggests that this air was likely recently transported from higher altitudes.
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